       Re: Mathematica gives bad integral ??

• To: mathgroup at smc.vnet.net
• Subject: [mg24332] Re: Mathematica gives bad integral ??
• From: "Kevin J. McCann" <Kevin.McCann at jhuapl.edu>
• Date: Sun, 9 Jul 2000 04:52:40 -0400 (EDT)
• Organization: Johns Hopkins University Applied Physics Lab, Laurel, MD, USA
• References: <8k3n38\$3pk@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```I suspect this has to do with branches of complex functions. I tried
using both Mathematica and the Schaum answer on definite integrals, e.g.
{x,1,2}, and got the same answers. Without spending a lot of time, I do
not see how to easily find the relationship between the two answers.

Kevin

"J.R. Chaffer" wrote:
>
> Hi,  this newbie gets erroneous results with Mathematica
> 4.0 (for students), with the following integral.  Hopefully
> someone can tell me why, and what I may be doing
> wrong.  I have tried "Assumptions -> x e Reals", or
> x > 0, with same results.  Integral in question is,
>
> Integrate[1/Sqrt[1-Sin[2x]]]
>
> The result is somewhat involved, instead of the expected
> result (Schaum, "Calculus" 4E, p. 297),
>
>   integral = - (1/Sqrt)Log[Abs[Csc[Pi/4-x]-Cot[Pi/4-x]]]
>
> One expects to get differing forms with any computer
> algebra system, since there are so many equivalent forms
> of algebraic expressions.  However, Mathematica's form
> and the Schaum (correct) form differ by significant
> numerical values, as plotting shows (i.e., not some E-16
> or some such).
>
> Further, and what really seems wrong, is that when one
> differentiates Mathematica's result for the integral, one
> does NOT get the original integrand, or anything even
> close, numerically.
>
> So, I am confused.  Anyone who knows the explanation
> would be welcome to share it.
>
> Thank you.
>
> John Chaffer

```

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